Effective actions for spin ladders

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We derive a path-integral expression for the effective action in the continuum limit of an AFM Heisenberg spin ladder with an arbitrary number of legs. The map is onto an O(3) nonlinear σ-model (NLσM) with the addition of a topological term that is effective only for odd-legged ladders and half-odd integer spins. We derive the parameters of the effective NLσM and the behaviour of the spin gap for the case of even-legged ladders.